First baby, didn't sleep through until he was about 3, and even then he still woke up at 5 and got into bed with us.
Second baby, 3 weeks.
This emphasis on sleeping through is really misleading I think. They'll do it when they're ready. The more important thing is how you can make changes to make sure you're getting enough sleep. One method is to wait until your baby sleeps through, but that could be ages so not the best solution. In the meantime, what else can you do to make sure you're as rested as possible given the circumstances? That's the most important question.
For us the magic answer was co-sleeping. Although DS woke throughout the night, I hardly needed to wake to feed him and we fell back to sleep together, so no need for settling at all. I was waking several times a night, sure, but never having to get out of bed or spend any time waiting for a baby to sleep.
For DD, there wasn't enough room in the bed to co-sleep (as DS was still getting in in the early hours) so we got a 3-sided cot. Best purchase ever. In reality, she slept on the edge of the bed most of the time, but safely as if she rolled off, she was just rolling into the cot.
I found a very reasonably priced on on German Amazon (courtesy of a mumsnetter recommendation) about £110 for the cot, mattress, bumpers and delivery IIRC. I'll have a look and post a link.
If you do cosleep, you should research safer ways to cosleep as there's guidance on this.